A dynamic model of size-dependent reproductive effort in a sequential hermaphrodite: A counterexample to Williams's conjecture

In 1966, G. C. Williams showed that for iteroparous organisms, the level of reproductive effort that maximizes fitness is that which balances the marg inal gains through current reproduction against the marginal losses to expe cted future reproduction. When, over an organism's lifetime, the value of f uture reproduction declines relative to the value of current reproduction, the level of effort allocated to current reproduction should always increas e with increasing age. Conversely, when the value of future reproduction in creases relative to the value of current reproduction, the level of effort allocated to current reproduction should decrease or remain at zero. While this latter pattern occurs commonly in species that exhibit a delayed age a t first reproduction, it may also occur following an initial period of repr oduction in some sex-changing organisms that experience a dramatic increase in reproductive potential as they grow larger. Indeed, this schedule of re productive effort is predicted by models of "early" sex change; however, th ese models may arrive at this result incidentally because they consider onl y two reproductive states: on and off. In order to examine the schedule of reproductive effort in greater detail in a system where the potential repro ductive rate increases sharply, we adapt the logic and methods of time-depe ndent dynamic-programming models to develop a size-dependent model of repro ductive effort for an example species that experiences a dramatic increase in reproductive potential at large sizes: the bluehead wrasse, Thalassoma b ifasciatum. Our model shows that the optimal level of reproductive effort w ill decline with increasing size or age when increases to the residual repr oductive value outpace the increases to current reproductive potential. Thi s result confirms the logic of Williams's analysis of optimal life historie s, while offering a realistic counterexample to his conjecture of ever-incr easing allocation to current reproduction.